Waves such as ultra low frequency waves, microwaves and visible light waves are widely used in a large range of technologies. For example, low frequency waves are used in geophysical exploration, microwaves are used in radar and wireless technologies and light waves are used in optical technologies. As such, it is important to be able to accurately model how waves move through a space, in order to be able to understand and use the waves effectively.
The finite difference time domain (FDTD) method is known to be effective at modelling propagation of waves within a space. The FDTD method is an iterative method which operates by dividing a space to be modelled into a plurality of magnetic (H) and electric (E) points. Discretising the space in this way allows a continuous wave to be modelled in a discrete space. Each iteration of the FDTD method calculates either values for all H points or values for all E points and movement of a wave through the space is modelled iteratively. In order to model a continuous wave in this way, half iterations are used so that one time step takes the form of two half iterations, with each iteration updating one of the H and E values. It will be appreciated that in the real world, waves propagate through an infinite space. Modelling an infinite space is not computationally possible using current computing techniques and as such, FDTD spaces in which waves are modelled must be bounded. This is problematic as boundaries cause reflection of the wave which would not occur in the real world, given that in the real world the boundary is not present. As such, it is desirable to use boundaries that do not cause reflection.
One known way of bounding a FDTD space used for modelling a wave which addresses some of the problems set out above is to use a Perfectly Matched Layer (PML). The PML can be used as an absorbing boundary condition (ABC) such that waves that meet the boundary are absorbed rather than reflected, and use of the PML as an ABC has been shown to allow effective modelling of how a wave propagates in the real world. However, use of the PML as an ABC is computationally expensive.
A further ABC that has been proposed is the Huygens absorbing boundary condition (HABC). This is often used in combination with a Perfect Electrical Conductor (PEC) placed a small number of FDTD points outside of the HABC. The method using an HABC and PEC is computationally inexpensive and effective in some circumstances, however it is known that values indicating wave propagation at some FDTD points generated using this method do not always agree with theoretical values. A computationally inexpensive method of effectively modelling a wave in a space is therefore desirable.